Fundamentals of Physics Extended (10th Edition)

by
Halliday, David; Resnick, Robert; Walker, Jearl

Published by
Wiley

ISBN 10:
1-11823-072-8

ISBN 13:
978-1-11823-072-5

Chapter 7 - Kinetic Energy and Work - Problems - Page 171: 13c

Answer

$Work$ $Done = -5.8\times10^{4}$ $J$

Work Step by Step

We know that:
$W= F.d$
To find W, we need the values of distance and the force.
Since they are travelling with an initial velocity of $37m/s$ and with a retardation of $2m/s^{2}$, we get the distance $d$ by using
$v^{2}= v_{o}^{2}+2ad$
Plugging respective values in it, we get:
$0^{2}=37^{2}+2(−2)d$
$\frac{−37^{2}}{−4}=d$
$d ≈3.4×10^{2}$ $m$
Now, we need to find the force.
We know;
$F= ma$
So plugging in the values of mass and acceleration, we get:
$F=85\times(-2)= -170$ $N$
Now putting the values of force and distance in the expression $W=F.d$ and solving we get:
$W= (-170)\times 3.4\times 10^{2}= -57800J$
$W= -5.78\times 10^{4}J\approx -5.8\times 10^{4}$ $J$